Mimic Sculpting Shader/Light setup for Render
If you want to render it in Cycles or Eevee, you can use this setting which allows to render a matcap:



The principle is to project the faces normal into the camera space so that we can hit the matcap texture by centering the projection using the mapping node, as a matcap texture looks like this:



You can choose the shader: here diffuse is used, but so the rendering is affected by other lights and shadows. If you want to avoid that, use the emission shader.

Matcap textures available in Blender can be found in your Blender installation path in '2.80\datafiles\studiolights\matcap'.

You can also use Workbench render engine. But in this case, all objects will have the same rendering: